The transmission probabilities for a particle through a barrier whose width and height are such that 2 L 2 m U 0 ℏ = 5 , when E U 0 = 0.4 and E U 0 = 0.6 .

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Answer 1

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Chapter 6, Problem 33E

(a)

To determine

The transmission probabilities for a particle through a barrier whose width and height are such that 2L2mU0ℏ=5 , when EU0=0.4 and EU0=0.6 .

(b)

To determine

The transmission probabilities for a particle through a barrier whose width and height are such that 2L2mU0ℏ=50 , when EU0=0.4 and EU0=0.6 .

(c)

To determine

The transmission probabilities for a particle through a barrier whose width and height are such that 2L2mU0ℏ=500 , when EU0=0.4 and EU0=0.6 .

(d)

To determine

The claim that the tunneling probability is a far more sensitive function of E when the tunneling probability is small, is correct.

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An electron having total energy E = 4.50 eV approaches a rectangular energy barrier with U = 5.00 eV and L = 950 pm as shown. Classically, the electron cannot pass through the barrier because E < U. Quantum- mechanically, however, the probability of tunneling is not zero. (a) Calculate this probability, which is the transmission coefficient. (b) To what value would the width L of the potential barrier have to be increased for the chance of an incident 4.50-eV electron tunneling through the barrier to be one in one million?

An electron with kinetic energy E = 3.10 eV is incident on a barrier of width L = 0.230 nm and height U = 10.0 eV (a) What is the probability that the electron tunnels through the barrier? (Use 9.11 10-31 kg for the mass of an electron, 1.055 ✕ 10−34 J · s for ℏ, and note that there are 1.60 ✕ 10−19 J per eV.) b) What is the probability that the electron is reflected? What If? For what value of U (in eV) would the probability of transmission be exactly 25.0% and 50.0%? c) 25.0% d) 50.0%

Answer 2

Question

Chapter 6, Problem 33E

(a)

To determine

The transmission probabilities for a particle through a barrier whose width and height are such that 2L2mU0ℏ=5 , when EU0=0.4 and EU0=0.6 .

(b)

To determine

The transmission probabilities for a particle through a barrier whose width and height are such that 2L2mU0ℏ=50 , when EU0=0.4 and EU0=0.6 .

(c)

To determine

The transmission probabilities for a particle through a barrier whose width and height are such that 2L2mU0ℏ=500 , when EU0=0.4 and EU0=0.6 .

(d)

To determine

The claim that the tunneling probability is a far more sensitive function of E when the tunneling probability is small, is correct.

Expert Solution & Answer

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Answer 3

Question

Chapter 6, Problem 33E

(a)

To determine

The transmission probabilities for a particle through a barrier whose width and height are such that 2L2mU0ℏ=5 , when EU0=0.4 and EU0=0.6 .

(b)

To determine

The transmission probabilities for a particle through a barrier whose width and height are such that 2L2mU0ℏ=50 , when EU0=0.4 and EU0=0.6 .

(c)

To determine

The transmission probabilities for a particle through a barrier whose width and height are such that 2L2mU0ℏ=500 , when EU0=0.4 and EU0=0.6 .

(d)

To determine

The claim that the tunneling probability is a far more sensitive function of E when the tunneling probability is small, is correct.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 4

Question

Chapter 6, Problem 33E

(a)

To determine

The transmission probabilities for a particle through a barrier whose width and height are such that 2L2mU0ℏ=5 , when EU0=0.4 and EU0=0.6 .

(b)

To determine

The transmission probabilities for a particle through a barrier whose width and height are such that 2L2mU0ℏ=50 , when EU0=0.4 and EU0=0.6 .

(c)

To determine

The transmission probabilities for a particle through a barrier whose width and height are such that 2L2mU0ℏ=500 , when EU0=0.4 and EU0=0.6 .

(d)

To determine

The claim that the tunneling probability is a far more sensitive function of E when the tunneling probability is small, is correct.

Expert Solution & Answer

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Answer 5

Chapter 6, Problem 33E

(a)

To determine

The transmission probabilities for a particle through a barrier whose width and height are such that 2L2mU0ℏ=5 , when EU0=0.4 and EU0=0.6 .

(b)

To determine

The transmission probabilities for a particle through a barrier whose width and height are such that 2L2mU0ℏ=50 , when EU0=0.4 and EU0=0.6 .

(c)

To determine

The transmission probabilities for a particle through a barrier whose width and height are such that 2L2mU0ℏ=500 , when EU0=0.4 and EU0=0.6 .

(d)

To determine

The claim that the tunneling probability is a far more sensitive function of E when the tunneling probability is small, is correct.

Answer 6

Chapter 6, Problem 33E

(a)

To determine

The transmission probabilities for a particle through a barrier whose width and height are such that 2L2mU0ℏ=5 , when EU0=0.4 and EU0=0.6 .

Answer 7

Chapter 6, Problem 33E

(a)

To determine

The transmission probabilities for a particle through a barrier whose width and height are such that 2L2mU0ℏ=5 , when EU0=0.4 and EU0=0.6 .

Answer 8

(b)

To determine

The transmission probabilities for a particle through a barrier whose width and height are such that 2L2mU0ℏ=50 , when EU0=0.4 and EU0=0.6 .

Answer 9

(b)

To determine

The transmission probabilities for a particle through a barrier whose width and height are such that 2L2mU0ℏ=50 , when EU0=0.4 and EU0=0.6 .

Answer 10

(c)

To determine

The transmission probabilities for a particle through a barrier whose width and height are such that 2L2mU0ℏ=500 , when EU0=0.4 and EU0=0.6 .

Answer 11

(c)

To determine

The transmission probabilities for a particle through a barrier whose width and height are such that 2L2mU0ℏ=500 , when EU0=0.4 and EU0=0.6 .

Answer 12

(d)

To determine

The claim that the tunneling probability is a far more sensitive function of E when the tunneling probability is small, is correct.

Answer 13

(d)

To determine

The claim that the tunneling probability is a far more sensitive function of E when the tunneling probability is small, is correct.

Answer 14

Expert Solution & Answer

Answer 15

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Answer 16

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Answer 17

Ch. 6 - Prob. 1CQ Ch. 6 - Prob. 2CQ Ch. 6 - Prob. 3CQ Ch. 6 - Prob. 4CQ Ch. 6 - Prob. 5CQ Ch. 6 - Prob. 6CQ Ch. 6 - Prob. 7CQ Ch. 6 - Prob. 8CQ Ch. 6 - Prob. 9CQ Ch. 6 - Prob. 10CQ

The transmission probabilities for a particle through a barrier whose width and height are such that 2 L 2 m U 0 ℏ = 5 , when E U 0 = 0.4 and E U 0 = 0.6 .

Solution Summary: The author explains the transmission probabilities for particle through a barrier whose width and height are such that 2Lsqrt2mU_0hslash =5

Concept explainers

The transmission probabilities for a particle through a barrier whose width and height are such that 2L2mU0ℏ=5 , when EU0=0.4 and EU0=0.6 .

The transmission probabilities for a particle through a barrier whose width and height are such that 2L2mU0ℏ=50 , when EU0=0.4 and EU0=0.6 .

The transmission probabilities for a particle through a barrier whose width and height are such that 2L2mU0ℏ=500 , when EU0=0.4 and EU0=0.6 .

The claim that the tunneling probability is a far more sensitive function of E when the tunneling probability is small, is correct.

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